Mystics & Statistics

The Source of the U.S. Army Three-to-One Rule

Oddly enough, 1991 was when this rule was first published, that we are aware of. It was published in the CGSC (Command and General Staff College) Student Text 100-9: Techniques and Procedures for Tactical Decision Making dated July 1991. There may have been work or materials prepared before then that we are not aware of.

The actual statement in that publication is that “Historical experience has shown that a defender has approximately a 50-50 probability of successfully defeating an attacking force approximately three times his equivalent strength.” The publication then goes on to recommend that for planning purposes that they “Therefore, as our start part, we will attempt to defend on each avenue of approach with, roughly, a 1-to-3 force rations expressed as a US unit defending against the next higher level enemy unit. For example, a US battalion would defend against an enemy regiment. There are only tools for the plan. Table 3-2 shows the preferred minimum planning ratios used to initially array forces.” The key here is the words “initially” and “to start with.” When deploying out a force, seeing up a blocking force that may be initially outnumbered three-to-one in an planned deployment does not mean that it will be outmatched in combat power by three-to-one as the battle develops. It is possible to reinforce the unit, provide it with artillery or air support, or withdraw to a more favorable position. So, the guidance that forces should be arrayed one level lower than the expected opposition is not bad guidance, even though one of the arguments made in that 1991 document supporting this is clearly wrong. The problem is that this rule is now repeated in other army documents without fully clarifying that this is just a planning factor for initial dispositions. It is also serving as the basis for charts in manuals and informal casualty estimation and modeling procedures. The army now commonly publishes the following table (from the proposed ATP 5-0.2, 31 July 2019):

Historical minimum planning ratios

Friendly Mission                     Friendly: Enemy

Hasty defend                          1:2.5

Deliberate defend                   1:3

Hasty attack                            2.5:1

Deliberate attack                     3:1

Delay                                       1:6

Counterattack                         1:1

Penetration (lead element)      18:1

 

This table, as shown by the data leave the impression that you need to have three-to-one odds to attack and that one-to-three odds is sufficient for defense. This would be the wrong impression to give. To claim that it is “historical” gives it more authority than it deserves, as the historical data in fact does not support this table. They are “minimum planning” factors, and that needs to properly stressed.

The bigger problem is that you fight as your train. So, if the officer corps is trained that you need at least a three-to-one force ratio to have a 50% chance of winning, then what kind of war planning and offensive action is now being envisioned? In World War II, the most common attack in our database are those at odds 1.00- to 1.49-to-one and they win 63% of the time. In the post-World War II engagements, the most common attack is done at 0.54- to 0.97-to-1 and the attacker wins 75% of the time (20 cases). So to what reality are we training our officers? Are we training the next generation of George B. McCellans?

Post-World War II Cases from the Division-level Database

We have 66 engagements in our database from after World War II. There are 51 cases from the Arab-Israeli Wars and 15 cases from the 1991 Gulf War.

Arab-Israeli Wars 1956-1973 (51 cases)

Force Ratio…………………Percent Attacker Wins………………..Number of Cases

0.54 to 0.97-to-1……………….76%…………………………………………….17

1.00 to 1.47-to-1……………….82……………………………………………….11

1.51 to 1.99-to-1……………….50…………………………………………………4

2.04 to 2.25-to-1……………….50…………………………………………………4

2.90-to-1……………………….100…………………………………………………1

3.03 to 3.59-to-1…………………0…………………………………………………2

3.50 to 3.96-to-1……………….25…………………………………………………4

4.11 to 5.87-to-1……………….40…………………………………………………5

6.06-to-1……………………….100…………………………………………………1

8.02 to 12.18-to-1…………….100…………………………………………………2

 

Now, this data is highly variable, with the largest number of attacks being conducted at less than one-to-one odds and the attacker winning 76% of the time. This is because of a significant difference in the combat capability of Israeli forces compared to the Egyptians, Syrians and other Arab armies that they are engaged with. This difference is well documented and discussed in more depth in my book War by Numbers. Of the 17 attacks at less than one-to-one odds, 16 were conducted by the Israelis and only one attack was conducted by the Arab armies. The Iraqi attack at those low odds was resoundingly defeated (Tel el Hara, 11 October 1973).

There is a similar performance disparity between the German and the Soviet armies in 1943. This also affects the force ratio data from World War II. We will separate these cases out by who the attacker is just to clarify the results. In the case of the Gulf War, the difference in morale, motivation and performance of the two armies were extremely disparate. This is a fairly extreme case, although not the only such case in history.

Gulf War (1991):

Force Ratio…………………..Percent Attacker Wins…………………Number of Cases

0.20 to 0.21…………………………0…………………………………………………..2

0.64 to 0.93………………………..67…………………………………………………..3

1.10 to 1.16………………………100…………………………………………………..2

None between 1.16 and 2.47

2.47……………………………….100………………………………………………….1

2.60 to 2.86………………………100………………………………………………….5

3.00 to 3.26………………………..50………………………………………………….2

 

One is hesitant to draw any conclusions from this data. The one attack that failed at three-to-one was the Iraqi Army attack at Khafji 29 January – 1 February 1991. In fact, all four failed attacks in the data set occurred when the Iraqis were attacking.

Anyhow, these databases can certainly be expanded and further analysis can be done, but good luck finding the three-to-one rule in this data that results in the defender winning 50% of the time. It is clear that from 1600 to 1991 that the attacker won more often than not at two-to-one odds or even lower, depending on the period and the forces involved. There is really no historical evidence supporting the Army version of this rule that I know of. I have been in this industry for over three decades and have not seen such evidence. I am not aware of any databases the size, depth or range of ones used here. If this historical data does not establish the rule, then where is the historical data that does?

The World War II Cases from the Division-level Database

There are 576 cases from World War II in our division-level database. There are no engagements from 1939, only two from 1940, seven from 1941, one from 1942 and the rest are from 1943-45.

World War II (576 cases) – complete data set

Force Ratio…………………….Percent Attacker Wins……………….Number of Cases

0.25 to 0.49………………………22%………………………………………………..9

0.50 to 0.98………………………30…………………………………………………50

1.00 to 1.49………………………55……………………………………………….128

1.50 to 1.96………………………61……………………………………………….117

2.01 to 2.49………………………73…………………………………………………48

2.52 to 2.99………………………82…………………………………………………44

3.00 to 3.49………………………76…………………………………………………41

3.50 to 3.98………………………85…………………………………………………26

4.06 to 5.86………………………68…………………………………………………59

6.17 to 7.90………………………87…………………………………………………15

8.20 to 17.87……………………100…………………………………………………20

 

This clearly makes our point in spades about the U.S. Army three-to-one rule. Above one-to-one odds the attacker wins over half the time and above two-to-one odds the attacker wins over 70% of the time. This is the un-culled data set. The culled data set with 102 cases removed that are “limited action,” limited attack” or “other” consists of only 474 cases. It shows the following:

World War II (474 cases) – culled data set

Force Ratio…………………Percent Attacker Wins…………………Number of Cases

0.25 to 0.49……………………..25%………………………………………………..8

0.50 to 0.98……………………..43………………………………………………….35

1.00 to 1.49……………………..63………………………………………………..111

1.50 to 1.96……………………..68………………………………………………..102

2.01 to 2.49……………………..83………………………………………………….41

2.52 to 2.99……………………..82………………………………………………….39

3.00 to 3.49……………………..79………………………………………………….33

3.50 to 3.98……………………..84………………………………………………….25

4.06 to 5.86……………………..77………………………………………………….48

6.17 to 7.90……………………..87………………………………………………….15

8.20 to 17.87…………………..100………………………………………………….15

22.84-198.69…………………..100…………………………………………………..2

 

Again, no surprises in this data, and of course, it parallels the patterns seen in the previous data sets.

The World War I Cases from the Division-level Database

There are several major periods of covered by this 752 cases division-level database, so let us separate them out. The periods covered are:

Era ………………………………………………Number of Cases

Russo-Japanese War (1904-1905)……………….3

The Balkan Wars (1912)……………………………1

World War I (1914-1918)…………………………25

Between the wars (1938)………………………….1

World War II (1939-1945)………………………576

Arab-Israeli Wars (1956 – 1973)………………..51

Gulf War (1991)………………,………………….15

 

The U.S. Army Three-to-One Rule versus the 752 Case Division-level Data Base 1904-1991

Now, both World War I and World War II are so massive that with a diligent research effort, thousands of engagements could be assembled. This does take time. Our post-World War II includes almost every significant division-level engagement from the Arab-Israeli fighting of 1956, 1967, 1968 and 1973. The Gulf War category includes every significant division-level engagement from 1991. Let us look at each of them in turn:

World War I and others (30 cases)

 

Force Ratio……………………Percent Attacker Wins……………..Number of Cases

0.67 to 0.99-to-1………………..29%…………………………………………..7

1.01 to 1.47-to-1………………..11……………………………………………..9

1.58 to 1.80-to-1………………….0……………………………………………..2

2.00 to 2.13-to-1………………..67……………………………………………..3

2.50 to 2.80-to-1………………..67……………………………………………..3

3.00 to 3.20-to-1………………..33……………………………………………..3

4.04 to 4.38-to-1………………..50……………………………………………..2

6.32-to-1………………………..100……………………………………………..1

 

Note that the attacker is winning to majority of the time at two-to-one odds and higher. The 33% wins in the three-to-one category consists of one victory and two drawn engagements (Bazentin Ridge from the Somme and First Dardanelles Landing from Gallipoli). In both of these cases the attacker advanced, although the engagement is coded as a draw. These three cases do not make a strong argument. This data collection is too small to draw any real conclusions from. The database could certainly be expanded to thousands of cases given time and effort. We also have a collection of engagements from World War I at brigade- and battalion-level and a number of engagements above division-level. These will be explored later.

TDI Friday Read: Battalion-Level Combat Model Validation

Today’s Friday Read summarizes a series of posts detailing a validation test of the Tactical Numerical Deterministic Model (TNDM) conducted by TDI in 1996. The test was conducted using a database of 76 historical battalion-level combat engagements ranging from World War I through the post-World War II era. It is provided here as an example of how such testing can be done and how useful it can be, despite skepticism expressed by some in the U.S. operations research and modeling and simulation community.

Validating A Combat Model

Validating A Combat Model (Part II)

Validating A Combat Model (Part III)

Validating A Combat Model (Part IV)

Validating A Combat Model (Part V)

Validating A Combat Model (Part VI)

Validating A Combat Model (Part VII)

Validating A Combat Model (Part VIII)

Validating A Combat Model (Part IX)

Validating A Combat Model (Part X)

Validating A Combat Model (Part XI)

Validating A Combat Model (Part XII)

Validating A Combat Model (Part XIII)

 

The U.S. Army Three-to-One Rule versus the 752 Case Division-level Data Base 1904-1991

Our most developed database through is our division-level database of 752 cases covering combat from 1904 to 1991. As this addresses modern combat, it is a useful database for such a test. Of those 752 cases, we have the forces ratios and outcome for 672 of them. All the engagements previously discussed from ETO in 1944 and Kharkov and Kursk in 1943 are drawn from this database. As such, there is some overlap between these 672 cases and the 116 cases from ETO and 73 cases from the Eastern Front previously used. The data shows a very clear pattern related to force ratios.

Division-level Engagements 1904-1991 (672 cases)

Force Ratio…………………..Percent Attacker Wins………………Number of Cases

0.20 to 0.20-to-1………………..0%………………………………………………….2

0.25 to 04.9-to-1………………22…………………………………………………….9

0.50 to 0.99-to-1………………42…………………………………………………..77

1.00 to 1.49-to-1………………55…………………………………………………150

1.50 to 1.99-to-1………………59…………………………………………………123

2.00 to 2.49-to-1………………71…………………………………………………..56

2.50 to 2.99-to-1………………83…………………………………………………..53

3.00 to 3.49-to-1………………69…………………………………………………..48

3.50 to 3.98-to-1………………77…………………………………………………..30

4.06 to 5.87-to-1………………65…………………………………………………..66

6.06 to 7.90-to-1………………88…………………………………………………..17

8.20 to 17.87-to-1……………100…………………………………………………..22

 

This table drives home in spades the problem with the U.S. Army current interpretation of the three-to-one rule (50% chance of defender success). To start with, the attacker starts winning over half the time at 1.00 to 1.49-to-1 odds. By the time they get to 2.50 to 2.99-to-1 odds they are winning 83% of the time. It is quite clear from this data that the U.S. Army rule is wrong.

Now, this data is skewed a little bit by the inclusion of engagements with “limited action” or only “limited attack.” They include engagements where the attacker has a significant force ratio but conducted only an initial probing attack of battalion size. Sometimes those attacks did not succeed. So the success rate of some the higher odds engagements would actually be higher if these were eliminated. So, we ended up culling 102 of these engagements from the above table to produce the following table.  There is not a big difference in the results between this tighter table of 570 cases and the previous table of 672 cases. The primary difference is that the attacker tends to be more successful in all categories. All the culled engagements were from World War II.

Division-level Engagements, 1904-1991 (570 cases) – culled data set

 

Force Ratio………………….Percent Attacker Wins……………….Number of Cases

0.20 to 0.20-to-1………………..0%…………………………………………………2

0.25 to 04.9-to-1………………25……………………………………………………8

0.50 to 0.99-to-1………………52…………………………………………………..62

1.00 to 1.49-to-1………………62…………………………………………………133

1.50 to 1.99-to-1………………66…………………………………………………108

2.00 to 2.49-to-1………………80………………………………………………….49

2.50 to 2.99-to-1………………83………………………………………………….48

3.00 to 3.49-to-1………………70………………………………………………….40

3.50 to 3.98-to-1………………76………………………………………………….29

4.06 to 5.87-to-1………………73………………………………………………….55

6.06 to 7.90-to-1………………88………………………………………………….17

8.20 to 17.87-to-1……………100………………………………………………….17

56.20-109.98-to-1……………100…………………………………………………..2

 

Needless to say, this tighter data set is even further biased against the published U.S. Army three-to-one rule.

The U.S. Army Three-to-One Rule versus 49 U.S. Civil War battles

From 1st Alabama Cavalry, USV website (www.1stalabamacavalryusv.com). Alexander Lawrence was from Fayette County, Alabama and fought for the Union with the 1st Alabama Cavalry

As the three-to-one rule of thumb appears to have evolved out of the American Civil War (although not as published in FM 6-0), then we should probably look at just our Civil War battles in our database.

Among those 243 cases are 49 cases from the American Civil War. As the three-to-one rule may have evolved from that experience, let us looking at just those cases:

 Force Ratio……………………Percent Attacker Wins……………….Number of Cases

0.44 to 0.48-to-1…………………0%………………………………………………3

0.53 to 0.97-to-1………………..18……………………………………………….11

1.00 to 1.47-to-1………………..36……………………………………………….14

1.53 to 1.96-to-1………………..25……………………………………………….12

2.10 to 2.31-to-1………………..50…………………………………………………6

3.00-to-1……………………….100…………………………………………………1

5.00-to-1……………………….100…………………………………………………1

15.05-to-1……………………..100…………………………………………………1

 

The American Civil War is a very good test case for such an examination. Both officer corps were primarily trained at West Point (the U.S. military academy); both armies fought in the same style and doctrine; they used most of the same weapons, including the same muskets and same artillery; they were similar in culture; and they were similar in training, doctrine, background and capability. While some historical mythology has tried to make the southern Americans better fighters, it is hard to accept the argument that a farmer from North Carolina is a different, more motivated or a more capable fighter than a farmer from Pennsylvania. Most of the United States was rural. There wre also units raised to fight for the north from all of the southern states. This is about an equal comparison between two opponents that one is going to find.

The end results from these two tests are that the three-to-one rule as recorded in FM 6-0 clearly does not apply. In the case of the Civil War data at 2.10 to 2.31-to-1 odds the attacker is winning half the time. Where does one get the notion that at 3.00-to-1 odds the defender will win half the time? What historical data established that?

So the U.S. Army version of the three-to-one (meaning defender wins half the time) does not show up in the almost 400 years of history that we are examining here and does not show up in the American Civil War.

Validating A Combat Model (Part XIII)

Gun crew from Regimental Headquarters Company, U.S. Army 23rd Infantry Regiment, firing 37mm gun during an advance against German entrenched positions, 1918. [Wikipedia/NARA]

[The article below is reprinted from June 1997 edition of The International TNDM Newsletter.]

The Second Test of the Battalion-Level Validation:
Predicting Casualties Final Scorecard
by Christopher A. Lawrence

While writing the article on the use of armor in the Battalion-Level Operations Database (BLODB), I discovered that l had really not completed my article in the last issue on the results of the second battalion-level validation test of the TNDM, casualty predictions. After modifying the engagements for time and fanaticism. I didn’t publish a final “scorecard” of the problem engagements. This became obvious when l needed that scorecard for the article on tanks. So the “scorecards” are published here and are intended to complete the article in the previous issue on predicting casualties.

As you certainly recall, amid the 40 graphs and charts were six charts that showed which engagements were “really off.” They showed this for unmodified engagements and CEV modified engagements. We then modified the results of these engagements by the formula for time and “casualty insensitive” systems, we are now listing which engagements were still “off” after making these adjustments.

Each table lists how far each engagement was off in gross percent of error. For example, if an engagement like North Wood I had 9.6% losses for the attacker, and the model (with CEV incorporated) predicted 20.57%, then this engagement would be recorded as +10 to +25% off. This was done rather than using a ratio, for having the model predict 2% casualties when there was only 1% is not as bad of an error as having the model predicting 20% when there was only 10%. These would be considered errors of the same order of magnitude if a ratio was used. So below are the six tables.

Seven of the World War I battles were modified to account for time. In the case of the attackers we are now getting results with plus or minus 5% in 70% of the cases. In the case of the defenders, we are now getting results of plus or minus 10% in 70% of the cases. As the model doesn’t fit the defender‘s casualties as well as the attacker‘s, I use a different scaling (10% versus 5%) for what is a good fit for the two.

Two cases remain in which the predictions for the attacker are still “really off” (over 10%), while there are six (instead of the previous seven) cases in which the predictions for the defender are “really off” (over 25%).

Seven of the World War II battles were modified to account for “casualty insensitive” systems (all Japanese engagements). Time was not an issue in the World War II engagements because all the battles lasted four hours or more. In the case of the attackers, we are now getting results with plus or minus 5% in almost 75% of the cases. In the case of the defenders, we are now getting results of plus or minus 10% in almost 75% of the cases. We are still maintaining the different scaling (5% versus 10%) for what is a good fit for the two.

Now in only two cases (used to be four cases) are the predictions for the attacker really off (over 10%), while there are still five cases in which the predictions for the defender are “really off” (over 25%).

Only 13 of the 30 post-World War II engagements were not changed. Two were modified for time, eight were modified for “casualty insensitive” systems, and seven were modified for both conditions.

In the case of the attackers we are now getting results within plus or minus 5% in 60% of the cases. In the case of the defenders, we are now getting results within plus or minus 10% in around 55% of the cases. We are still maintaining the different scaling (5% versus 10%) for what is a good fit for the two.

We have seven cases (used to be eight cases) in which the attacker‘s predictions are “really off” (over 10%), while there are only five cases (used to be 10) in which the defender‘s casualty predictions are “really off” (over 25%).

Repetitious Conclusion

To repeat some of the statistics from the article in the previous issue, in a slightly different format:

The U.S. Army Three-to-One Rule versus 243 Battles 1600-1900

Now, at the time I wrote War by Numbers, I was not aware of this sentence planted in FM 6-0 and so therefore did not feel a need to respond to the “3-to-1 rule.” It is a rule of thumb, not completely without value, that had been discussed before. I thought this issue was properly understood in the U.S. analytical and defense community, therefore I did not feel a need to address it further. It turns out that I do. So, let me take a moment to tap into our databases and properly address this using all the resources at my disposal.

First of all, The Dupuy Institute has a database of 243 engagements from 1600-1900 called the Battles Data Base (BaDB). These are almost all field battles, where the two sides deployed their forces of tens of thousands of people and resolve their dispute that day. Of the 243 battles, only 40 of them last longer than a day. The largest engagement has the attacker fielding 365,000 men (Leipzig, 1813) and the smallest engagement had the defender fielding but 350 men (Majuba Hill, 1881).

As this rule of thumb evolved out of the U.S. Civil War, then an examination of historical field battles from 1600-1900 is particularly relevant. Looking at the force ratio for these battles shows:

Force Ratio…………………..Percent Attacker Wins………………..Number of Cases

0.26 to 04.9-to-1………………54%……………………………………………13

0.50 to 0.98-to-1………………54………………………………………………81

1.00 to 1.47-to-1………………56………………………………………………71

1.50 to 1.96-to-1………………63………………………………………………38

2.00 to 2.44-to-1………………50………………………………………………16

2.58 to 2.94-to-1………………57………………………………………………..7

3.00 to 3.43-to-1…………….100………………………………………………..5

3.75 to 3.76-to-1………………..0………………………………………………..2

4.00 to 4.93-to-1………………75………………………………………………..4

7.78 to 16.82-to-1……………..67………………………………………………..6

 

The pattern here is not particularly clear, as low odds attack, where the attacker is outnumbered, succeed over half the time, as do attacks at higher odds. Some of this is due to the selection of battles, some of this is due to the lack of regular trained armies, and some of this is due to the attacker choosing to attack because they have advantages in morale, training, experience, position, etc. that outweigh the numbers. But, the argument that is made in FM 6-0 that based upon historical data at three-to-one odds the defender wins 50% of the time is clearly not shown. For example, in this data set there are 12 cases between the odds of 2.50 to 3.50-to-1. Of those 12 cases, the attacker wins in 9 of them (75%). The three cases where the defender wins are: 1) Battle of Buena Vista in 1847 where Santa Anna’s Mexican Army attacked Zachary Taylor’s American Army at 2.94-to-1, 2) Battle of Inkeman in 1854 where the Russian Army attacked the French and British armies in Crimea at 2.63-to-1, and 3) Battle of Belfort in 1871 where the French Army attack the German Army at 2.75-to-1. One could certainly argue that in these three cases, the defenders held advantages in training, experience and overall combat effectiveness.

Next post will address the 49 American Civil War battles in our database.

Validating A Combat Model (Part XII)

[The article below is reprinted from April 1997 edition of The International TNDM Newsletter.]

The Second Test of the TNDM Battalion-Level Validations: Predicting Casualties
by Christopher A. Lawrence

FANATICISM AND CASUALTY INSENSITIVE SYSTEMS:

It was quite clear from looking at the battalion-level data before we did the validation runs that there appeared to be two very different loss patterns, based upon—dare I say it—nationality. See the article in issue 4 of the TNDM Newsletter, “Looking at Casualties Based Upon Nationality Using the BLODB.” While this is clearly the case with the Japanese in WWII, it does appear that other countries were also operating in a manner that produced similar casualty results. So, instead of using the word fanaticism, let’s refer to them as “casualty insensitive” systems. For those who really need a definition before going forward:

“Casualty Insensitive” System: A social or military system that places a high priority on achieving the objective or fulfilling the mission and o low priority on minimizing casualties. Such systems lend to be “mission obsessive” versus using some form of “cost benefit” method of weighing whether the objective is worth the losses suffered to take it.

EXAMPLES OF CASUALTY INSENSITIVE SYSTEMS:

For the purpose of the database, casualty sensitive systems were defined as the Japanese and all highly motivated communist-led armies. These include:

  • Japanese Army, WWII
  • Viet Mihn
  • Viet Cong
  • North Vietnamese
  • Indonesian

We have included the Indonesians in this list even though it was based upon only one example.

In the WWII and post-WWII period, one would expect that the following armies would also be “casualty insensitive”

  • Soviet Army in WWII
  • North Korean Army
  • Communist Chinese Army in Korea
  • Iranian “Pasdaran“

Data can certainly be found to test these candidates.

One could postulate that the WWI attrition multiplier of 4 that we used also incorporates the 2.5 “casualty insensitive” multiplier. This would imply that there was only a multiplier of 1.6 to account for other considerations, like adjusting to the impact of increased firepower on the battlefield. One could also postulate that certain nations, like Russia, have had “casualty insensitive” systems throughout their last 100 years of history. This could also be tested by looking of battles over time of Russians versus Germans compared to Germans versus British, U.S. or French. One could easily carry this analysis back to the Seven Years’ War. If this was the case, this would establish a clear cultural basis for the “casualty insensitive” multiplier, but to do so would require the TNDM to be validated for periods before 1900. This would all be useful analysis in the future, but is not currently budgeted for.

It was expected that the “casualty insensitive” multiplier of 2.5 derived from the Japanese data would be too high to apply directly to the armies. Much to our surprise, we found that this did not appear to be the case. This partially or wholly explained the under-prediction of the 15 of our 20 significantly under-predicted post-WWII engagements. Time would explain another one. And four were not explained.

The model noticeably underestimated all the engagements under nine hours except Bir Gifgafa I (2 hours). Pearls AFB (4.5) and Wireless Ridge (8 hours). It noticeably under-estimated all the 15 “fanatic” engagements. If the formulations derived from the earlier data were used here (engagements less than 4 hours and fanatic), then there are 17 engagements in which one side is “casualty insensitive” or in which the engagement time is less than 4 hours. Using the above formulations then 17 engagements would have their casualty figures changed.

The modified percent loss figures are the CEV predicted percent loss times the factor for “casualty insensitive” systems (for those 15 cases where it applies) and times the formulation for battles less than 4 hours (for those 9 cases where it applies).

Looking at the table at the top of the next page, it would appear that we are on the correct path. But to be safe, on the next page let’s look at the predictive value of the 13 engagements for which we didn’t redefine the attrition multipliers.

The 13 engagements left unchanged:

So, we are definitely heading in the right direction now. We have identified two model changes—time and “casualty insensitive.” We have developed preliminary formulations for time and for “casualty insensitive” forces. Unfortunately, the time formulation was based upon seven WWI engagements. The “casualty insensitive” formulation was based upon seven WWII engagements. Let’s use all our data in the first validation database here for the moment to come up with figures with which we can be more comfortable:

The highlighted entries in the table above indicate “casualty insensitive” forces. We are still struggling with the concept that having one side being casualty insensitive increases both sides’ losses equally. We highlighted them in an attempt to find any other patterns we were missing. We could not.

Now, there may be a more sophisticated measurement of this other than the brute force method of multiplying both sides by 2.5. This might include different multipliers depending on whether one is the fanatic vs non-fanatic side or different multipliers for attack or defense. First, I cannot find any clear indication that there should be a different multiplier for the attacker or defender. A general review of the data confirms that. Therefore, we are saying that the combat relationships between attacker and defender do not change in high intensity or casualty insensitive battles from those experienced in the norm.

What is also clear is that our multiplier of 2.5 appears to be about as good a fit as we can get from a straight multiplier. It does not appear that there is any significant difference between the attrition multiplier for types of “casualty insensitive” systems, whether they are done because of worship of the emperor or because the commissar will shoot slackers. Apparently the mode of fighting is more significant for measuring combat results than how one gets there, although certainly having everyone worship the emperor is probably easier to “administer.”

This still leaves us having to look at whether we should develop a better formulation for time.

Non-fanatic engagement of less than 4 hours:

For fairly obvious reasons, we are still concerned about this formulation for battles of less than one hour, as we have only one example, but until we conduct the second validation, this formulation will remain as is.

Now the extreme cases:

List of all engagements less than 4 hours where one side was fanatic:

It would appear that these formulations of time and “casualty insensitivity” have passed their initial hypothesis formulations tests. We are now willing to make changes to the model based upon this and run the engagements from the second validation data base to test it.

Next: Predicting casualties: Conclusions